Chapter 1

Statistics, Data, and Statistical Thinking

The Science of Statistics

Statistics – the science that deals with the collection, classification, analysis, and interpretation of information or data

Collection

Evaluation (classification, summary, organization and

analysis)

Interpretation

Collecting Data

Data Sources

1. Published source – books, journals, abstracts The Wall Street Journal, The Sporting News

2. Designed Experiment Often used for gathering information about an intervention

3. Survey Data gathered through questions from a sample of people

4. Observational Study Data gathered through observation, no interaction with units

Collecting Data

Common Sources of Error in Survey Data

Selection bias – exclusion of a subset of the population of interest prior to sampling

Non-response bias – introduced when responses are not gotten from all sample members

Measurement error – inaccuracy in recorded data. Can be due to survey design, interviewer impact, or a transcription error

Collecting Data

Sampling

1. Sampling is necessary if inferential statistics are to be used

2. Samples need to be representative Reflect population of interest

3. Random Sampling Most common sampling method to ensure sample is

representative

Ensures that each subset of fixed size is equally likely to be selected

Types of Statistical Applications in Business

Descriptive Statistics - describe collected data, utilize numerical and graphical methods to present the information

“51.4% of all credit card purchases inthe 1st quarter of 2003 were made with a Visa Card”

“The average Return-to-Pay Ratio of Financial Industry CEOs (2003) was 24.63”

Types of Statistical Applications in Business

Inferential Statistics - make generalizations about a group based on a subset (sample) of that group

“Services Industry CEOs are underpaid relative to CEOs in Telecommunications.”

Fundamental Elements of Statistics

Experimental Unit – object of interest example – graduating senior

Population – the set of units we are interested in learning about

example – all 1450 graduating seniors at “State U”

Variable – characteristic of a single experimental unit

example – age at graduation

Fundamental Elements of Statistics

Sample – subset of populationexample – 100 graduating seniors at “State U”

Statistical Inference – generalization about a population based on sample data

example – The average age at graduation is 21.9 (based on sample of 100)

Measure of reliability – statement about the uncertainty associated with an inference

Fundamental Elements of Statistics

Elements of Descriptive Statistical Problems

1. Population/sample of interest

2. Investigative variables

3. Numerical summary tools (charts, graphs, tables)

4. Pattern identification in data

Fundamental Elements of Statistics

Elements of Inferential Statistical Problems

1. Population of interest

2. Investigative variables

3. Sample taken from population

4. Inference about population based on sample data

5. Reliability measure for the inference

Types of Data

Quantitative Data

1. Measured on a naturally occurring numerical scale

2. Equal intervals along scale (allows for meaningful mathematical calculations)

3. Data with absolute zero (zero means no value) is ratio data (bank balance, grade)

4. Data with relative zero (zero has value) is interval data (temperature)

Types of Data

Qualitative Data

1. Measured by classification only

2. Non-numerical in nature

3. Meaningfully ordered categories identify ordinal data (best to worst ranking, age categories)

4. Categories without a meaningful order identify nominal data (political affiliation, industry classification, ethnic/cultural groups)

Types of Data

1. Different statistical techniques used for quantitative and qualitative data

2. Qualitative and Quantitative data can be used together in some techniques

3. Quantitative data can be transformed into Qualitative data through category creation

4. Qualitative data cannot be meaningfully transformed into Quantitative data